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Summary – Reduced natural system sequestration with warmer temperatures causes extra carbon to remain in the sky. Any cooling, natural or human-caused, reduces natural feedback emissions which reduces the atmospheric carbon burden. Geoengineering does indeed reduce the atmospheric Greenhouse gas concentration.

Abstract “Eleven coupled climate–carbon cycle models used a common protocol to study the coupling between climate change and the carbon cycle. The models were forced by historical emissions and the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emissions Scenarios (SRES) A2 anthropogenic emissions of CO2 for the 1850–2100 time period. For each model, two simulations were performed in order to isolate the impact of climate change on the land and ocean carbon cycle, and therefore the climate feedback on the atmospheric CO2 concentration growth rate. There was unanimous agreement among the models that future climate change will reduce the efficiency of the earth system to absorb the anthropogenic carbon perturbation. A larger fraction of anthropogenic CO2 will stay airborne if climate change is accounted for. By the end of the twenty-first century, this additional CO2 varied between 20 and 200 ppm for the two extreme models, the majority of the models lying between 50 and 100 ppm. The higher CO2 levels led to an additional climate warming ranging between 0.1° and 1.5°C.”

Friedlingstein et al., Climate–Carbon Cycle Feedback Analysis, Results from the C4MIP Model Intercomparison, Journal of Climate, July 15, 2006.
https://journals.ametsoc.org/view/journals/clim/19/14/jcli3800.1.xml

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